Vorticity transport in a corner formed by a solid wall and a free surface

Abstract

There is a growing body of literature in which turbulent boundary layer flow along a mixed-boundary corner formed by a vertical solid wall and a horizontal free surface has been examined. While there is consensus regarding the existence of weak secondary flows in the near corner region, there is some disagreement as to the exact nature and origin of these flows. In two earlier works by the authors, evidence was presented supporting the existence of a weak streamwise vortex which rotates in toward the wall at the free surface and down away from the surface along the wall. This ‘inner secondary vortex’ is accompanied by an ‘outer secondary flow’ which transports low-momentum boundary layer fluid up along the wall and outward at the free surface. The magnitudes of the cross-stream velocities associated with these secondary flows were measured to be on the order of 1% of the free-stream speed. In this paper, high-resolution DPIV measurements made in the cross-stream plane are presented. These clearly show the inner and outer secondary flows. The cross-stream vector fields allow computation of terms in the turbulent streamwise vorticity transport equation. These terms indicate mean vorticity transport at the free surface associated with the outer secondary flow. In addition there appears to be a balance between the wall-normal and free-surface-normal fluctuating vorticity reorientation terms.

Large-eddy simulations of ducts with a free surface

“…The origin of the inner secondary flow in the context of vorticity transport, the role played by the diverging surface current found when studying jets, wakes or boundary layers parallel to a free surface (Walker 1997), the vortex structures in a turbulent mixed-boundary corner, are examples of the questions not yet conclusively investigated. Many of the discrepancies are probably due to different set-ups in the different studies, as also mentioned by Grega et al (2002). High-resolution DPIV measurements made in the cross-stream plane by Grega et al (2002) using the same experimental apparatus as two earlier works by the authors, pointed out that there is an, as yet, undetermined source of streamwise vorticity particularly in the outer secondary flow region close to the free surface.…”

“…Many of the discrepancies are probably due to different set-ups in the different studies, as also mentioned by Grega et al (2002). High-resolution DPIV measurements made in the cross-stream plane by Grega et al (2002) using the same experimental apparatus as two earlier works by the authors, pointed out that there is an, as yet, undetermined source of streamwise vorticity particularly in the outer secondary flow region close to the free surface.…”

Effect of Gravity on Sheared Turbulence Laden With Bubbles or Droplets

“…These two effects are attributed to imbalances in the Reynolds stresses at the juncture. Numerical simulations and experiments by Grega et al, Grega et al (1995) Grega et al (2002), confirmed the existence of two streamwise vortices at the juncture region. The inner vortical structure flows towards the wall near the free surface and downwards along the wall.…”

Numerical simulation of turbulent flow through a straight square duct

“…The origin of the inner secondary flow in the context of vorticity transport, the role played by the diverging surface current found when studying jets, wakes or boundary layers parallel to a free surface [13], the vortex structures in a turbulent mixed-boundary corner, are examples of the questions, which are not yet conclusively investigated. Many of the discrepancies are probably due to the different set-ups in the different studies, as also mentioned by Grega et al [14]. High-resolution DPIV measurements [14] made in the cross-stream plane used the same experimental apparatus as two earlier works by the authors.…”

“…Many of the discrepancies are probably due to the different set-ups in the different studies, as also mentioned by Grega et al [14]. High-resolution DPIV measurements [14] made in the cross-stream plane used the same experimental apparatus as two earlier works by the authors. It was found that there was an, as yet, undetermined source of streamwise vorticity particularly in the outer secondary flow region closed to the free surface.…”